7 papers
A Proximal Point Semismooth Newton Algorithm for Structural Composite Cardinality Optimization
Penghe Zhang, Naihua Xiu, Houduo Qi
Many image-processing problems can be formulated as composite cardinality optimization (CCOP), whose objective is the sum of two convex terms and a cardinality function composed wi…
On the Stationary Duality of Structural Composite Cardinality Optimization
Penghe Zhang, Naihua Xiu, Houduo Qi
Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with…
Local Duality for Sparse Support Vector Machines
Penghe Zhang, Naihua Xiu, Houduo Qi
Due to the rise of cardinality minimization in optimization, sparse support vector machines (SSVMs) have attracted much attention lately and show certain empirical advantages over…
Composite Optimization with Indicator Functions: Stationary Duality and a Semismooth Newton Method
Penghe Zhang, Naihua Xiu, Houduo Qi
Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been…
Sparse SVM with Hard-Margin Loss: a Newton-Augmented Lagrangian Method in Reduced Dimensions
Penghe Zhang, Naihua Xiu, Hou-Duo Qi
The hard margin loss function has been at the core of the support vector machine (SVM) research from the very beginning due to its generalization capability.On the other hand, the…
iNALM: An inexact Newton Augmented Lagrangian Method for Zero-One Composite Optimization
Penghe Zhang, Naihua Xiu, Hou-Duo Qi
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, nonconvex optimization problems and it has attracted much attention recently. The augmented Lagrangian Method…
Global Convergence of Inexact Augmented Lagrangian Method for Zero-One Composite Optimization
Penghe Zhang, Naihua Xiu
We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely zero-one composite optimization prob…